On the Properties and Applications of Sine Type Ii Topp-Leone Kumaraswamy Distribution

Abstract

Statistical probability distributions constitute a fundamental component of data analysis 
by providing rigorous mathematical frameworks for modelling uncertainty and 
characterizing observed phenomena. However, many real-world datasets exhibit complex 
distributional features, including pronounced skewness, heavy-tailed behaviour, and non
monotonic hazard rate functions, which are often inadequately represented by 
conventional probability distributions. Addressing these challenges requires the 
development of more flexible statistical models capable of capturing diverse data 
structures while providing improved goodness-of-fit. In this study, a novel probability 
model, termed the Sine Type II Topp-Leone-Kumaraswamy (STII-TLKw) distribution, is 
proposed to accommodate complex data patterns encountered across a broad spectrum 
of scientific and engineering applications. The proposed distribution is formulated by 
integrating the flexibility of the Sine Type II generator with the Topp-Leone
Kumaraswamy family, resulting in a highly adaptable model with enhanced distributional 
properties. Its fundamental statistical characteristics, including the probability density 
function, cumulative distribution function, and other important mathematical properties, 
are derived and thoroughly investigated. Parameter estimation is performed using the 
Maximum Likelihood Estimation (MLE) method, while the finite-sample performance of 
the estimators is evaluated through an extensive Monte Carlo simulation study to assess 
their accuracy, consistency, and reliability. The practical applicability of the proposed 
distribution is further demonstrated using two real-life datasets. Model performance is 
assessed through standard information criteria and compared with several existing 
competing distributions. The STII-TLKw distribution consistently provides the best fit, 
yielding the lowest Akaike Information Criterion (AIC) values of 114.726 and 104.2888, 
together with the lowest Bayesian Information Criterion (BIC) values of 120.4631 and 
109.9024, respectively. These findings demonstrate that the proposed distribution 
offers superior modelling flexibility and predictive capability for complex empirical data.